Flavor Oscillation from the Two-Point Function

TL;DR

This paper introduces a formalism for analyzing flavor oscillations of unstable particles using two-point Green's functions, providing exact probability formulas applicable to various regimes including exotic ones.

Contribution

It develops a general framework based on two-point functions that unifies and extends existing oscillation formulas for neutrinos and mesons, allowing exploration of new parameter regimes.

Findings

Derived exact oscillation probability formulas

Verified consistency with known neutrino and meson results

Extended analysis to exotic parameter regimes

Abstract

We present a formalism for the flavor oscillation of unstable particles that relies only upon the structure of the time Fourier-transformed two-point Green's function. We derive exact oscillation probability and integrated oscillation probability formulae, and verify that our results reproduce the known results for both neutrino and neutral meson oscillation in the expected regimes of parameter space. The generality of our approach permits us to investigate flavor oscillation in exotic parameter regimes, and present the corresponding oscillation formulae.